dy 2. Locate the bifurcation values for the one-parameter family: = a- and draw the phase...
In Exercises 1-6, locate the bifurcation values for the one-parameter family and draw the phase lines for values of the parameter slightly smaller than, slightly larger than, and at the bifurcation values. dy α-ly 6. dt
4. Locate the bifurcation values for the one parameter family: y = y2 - 2y + 1. Draw the phase lines for the values of the parameter smaller, larger, and equal to each bifurcation value.
(1 point) Use the applet provided to draw a phase portrait for ' = -2x(1 - 2)(2-2) The above equation could represent a model of a population that can become extinct if it drops below a particular critical value. What is this critical value? (1 point) Determine the bifurcation value(s) for the one parameter family k = 0 help (numbers) Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your...
sketch phase lines for: dy/dt = y(y+3)^3(y-2)^2(y-5) sketch bifurcation diagram for: dy/dt = y(y^2+ α) where α is a parameter
Consider the family of differential equations dy/dx=y^3+ky+k^2 Are there any equilibrium solutions when k=0? Draw bifurcation diagram Draw phase diagram for when k=1/2 Does limit exist when k=1/2 and y(0)=0
2(a) Consider the one-parameter family of nonlinear ordinary differential equations -Ita-) where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium solutions using appropriate arrows. ii. Find all bifurcation points and classify them
2(a) Consider the one-parameter family of nonlinear ordinary differential equations -Ita-) where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium...
4 1. Fix a value c, and then consider the one parameter family Find the value of λ (in terms of c) for which this family encounter a saddle-node bifurcation
4 1. Fix a value c, and then consider the one parameter family Find the value of λ (in terms of c) for which this family encounter a saddle-node bifurcation
Section B - Answer any two questions. 2. (a) Consider the one-parameter family of nonlinear ordinary differential equations dr where a is a real parameter. i. Find all equilibrium points. ii. Sketch the bifurcation diagram, and indicate the behaviour of non- equilibrium solutions using appropriate arrows. ii. Find all bifurcation points and classify them. 10 Marks (b) Consider the second order differential equation i. Show that (1) can be written as the system of ordinary differential equations (y R for...
Bifurcation dy Consider the autonomous differential equation =y? - 2y + 8. We will begin by examining dt the equilibrium solutions of the equation for various values of the parameter 8 1. Find the equilibrium solutions of the equation for 8 = -4,-2, 0, 2, 4 and make a sketch of the phase line for each value. Determine the stability of each equilibria. 2. Use a computer or some other means to sketch some solution curves for each value of...
1. Consider the family of differential equations dy/dx = y^3 +
ky + k^3 .
Please Help me with it, thanks so much
1. Consider the family of differential equations de set = y2 + ky + k3. (a) Are there any equilibrium solutions when k = 0? If so, what are they? (b) Draw the bifurcation diagram. That is, sketch a graph of the critical values as a function of the parameter k. Clearly label the axes. (You may...